Troubling Maths for Racists and Nationalists

Geneticist Adam Rutherford teaches us that "there are no purebloods, only mongrels enriched by the blood of multitudes"

"2nd order differential eq 1" by recurrence is licensed under CC BY-NC-SA 2.0.

Nationalists, racists and populists like to make sweeping generalizations about large groups of people. In George Orwell’s famous words, they assume that “that human beings can be classified like insects and that whole blocks of millions or tens of millions of people can be confidently labelled ‘good’ or ‘bad’.”

British geneticist Adam Rutherford blows up the whole assumption with some very simple maths in an excellent book called How to Argue with a Racist (link below). We all know that we have two parents, four grandparents, eight great-grandparents and so on, with the numbers doubling in every generation (defined as 25 to 30 years). As we saw in the post on exponential growth, doubling a number many times can quickly generate results that appear weird to our intuitions.

Rutherford says that when you go back 500 years, you have 1,048,576 ancestors. When you go back 1,000 years, the number is 1,099,511,627,776. There have only been around 107 billion members of our species, “give or take a billion or so,” over the whole of our history. If we each have more than a trillion ancestors around 1,000 years ago, that is more than ten times as many people as ever lived.

Wait! What? Rutherford explains that it is best to think of us all as having a trillion positions on our family trees when we go back 1,000 years. The positions are then occupied by the same indivduals multiple times.

Rutherford writes: “The last common ancestors of all people with longstanding European ancestries lived only 600 years ago - meaning that if we could draw a perfect complete family tree for all Europeans, at least one branch on each tree would pass through a single person who lived around 1400 CE. This person would appear on all our family trees, as would all of their ancestors.”

The geneticist then gives an example to explain this point. A television show discovered that actor Danny Dyer was 22 generations descended from Edward III, a fourteenth-century British king. Rutherford says that there is a 100% chance that anyone with British ancestry is also descended from Edward III.

The maths gets scarier for racists and nationalists the further back you go. Rutherford says that any European who lived in the tenth century and has European descendants alive today will be the ancestor of all contemporary people of European descent.

The geneticist says that this is “a brain-scrambling concept” for the general public. This is particularly the case when he points out that everyone alive today is descended from every member of the global population who had descendants around 3,400 years ago - a startlingly recent date. However, he also says that the distribution of the positions on the family tree will be different. So, “a Chinese woman or man will have far fewer southern African ancestors than East Asian, and vice versa. But they will have some, and each of those ancestors has an equal relationship with their living descendants regardless of where on Earth they lived and died.”

The conclusions are staggering. “Every racist has African, Indian, Chinese, Native American, aboriginal Australian ancestors, as well as everyone else, and not just in the sense that humankind is an African species in deep prehistory, but at a minimum from classical times, and probably much more recently. Racial purity is a pure fantasy. For humans there are no purebloods, only mongrels enriched by the blood of multitudes.”

The fact that underlies this conclusion is very simple: People have always moved around, had sex (willingly or unwillingly) and made babies. These babies then grow up as members of certain communities. Some of them also move around and/or have sex with people from other communities (willingly or unwillingly) and make their own babies. And so on for many generations. Our species evolved maybe 300,000 years ago. That is more than 12,000 generations. Some communities can remain isolated for multiple generations, but not forever. Over such a long time scale, it only needs a little mixing each generation for us all to end up as distant cousins.

We can see this clearly with the Khoisan people of Africa, who are noticeably lighter skinned than other populations around them. This skin colour is associated with a gene that appears to have been introduced via migration back into Africa during the last 2,000 years. It is the same gene that is common within Europe. The gene provided some kind of selective advantage to the Khoisan and flourished in a new context. But, just as the Khoisan people have European ancestry, all Europeans also have Khoisan ancestry.

Strangely enough, “genetic shuffling” complicates the story even further. We get half our genome from our mother and half from our father. However, when we have kids ourselves, we only pass on half our genome. Some of it gets lost. Going back 11 generations, you will only carry DNA from half your ancestors. So, you might not actually be genetically related to many of your ancestors, even if you carry the same surname. Nationalists and other snobs might want to go and have a little lie down at this point.

The fundamental connection of all humanity is one of the big themes of this blog. Rutherford’s book helps build the case with some simple maths. It is well worth reading. Later chapters are skeptical about a purely genetic basis for Jewish over-representation in Nobel prizes, the dominance of sprinting by the descendants of West African slaves or East African excellence in long-distance running. The comments are open. See you next week!

Further Reading

How to Argue with a Racist by Adam Rutherford

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